how can this be wrong?

[red and white kop!]

a particle is moving along a straight line with constant acceleration. in an interval of T seconds it moves D metres; in the next interval of 3T seconds it moves 9D metres. how far does it move in a further interval of T seconds?

so I calculated the acceleration pretty simply, the velocity increased by 2D/T over 3T, so the constant acceleration is 2/3DT^-2. using this I calculated the distance travelled over the next interval of T seconds as being 0.5(3 + 3 + 2/3) = 20/6 D metres
the book says 5D metres. where did i go wrong?

 

[tkhunny]

You are neglecting the nature of your information. It is a little discontinuous.

In the first T, you travel D. This makes the AVERAGE velocity D/T. Since acceleration is constant, the value D/T is attained ONLY @ T/2

In the next 3T, you travel 9D. This makes the AVERAGE velocity 9D/3T = 3D/T. Since acceleration is constant, the value 3D/T is attained ONLY @ 5T/2

Finally, (3D/T - D/T)/(5T/2 - T/2) = (2D/T)/(4T/2) = (2D/T)/(2T) = D/T^2

You were not accelerating fast enough. We would expect, then, that your value would be less than appropriate. Indeed, 20/6 < 5

 

[Deleted member 4993]

a particle is moving along a straight line with constant acceleration. in an interval of T seconds it moves D metres; in the next interval of 3T seconds it moves 9D metres. how far does it move in a further interval of T seconds?

so I calculated the acceleration pretty simply, the velocity increased by 2D/T over 3T, so the constant acceleration is 2/3DT^-2. using this I calculated the distance travelled over the next interval of T seconds as being 0.5(3 + 3 + 2/3) = 20/6 D metres
the book says 5D metres. where did i go wrong?

The equation to use for linear motion with constant acceleration is:

S = ut + 1/2* a * t[sup:3v71ti0g]2[/sup:3v71ti0g](where S = distance travelled, u = speed at time = 0, a = acceleration and t = elapsed time)

t = T ? S = D ? D = uT + a/2*T[sup:3v71ti0g]2[/sup:3v71ti0g]

t = 4T ? S = 10D? 10D = 4uT + 8*a*T[sup:3v71ti0g]2[/sup:3v71ti0g] ? 6D = 6*a*T[sup:3v71ti0g]2[/sup:3v71ti0g] ? a = D/T[sup:3v71ti0g]2[/sup:3v71ti0g]? u = D/(2T)

at t = 5T

S = D/(2T)*5T + 1/2 * D/T[sup:3v71ti0g]2[/sup:3v71ti0g] * 25 * T[sup:3v71ti0g]2[/sup:3v71ti0g] = 15 D

and so on....